SOLUTION: Write an equation in standard form of the line with the given x-intercept and y-intercept. x-intercept -3 y-intercept -5 PLEASE HELP!

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Question 117172: Write an equation in standard form of the line with the given x-intercept and y-intercept.
x-intercept -3
y-intercept -5
PLEASE HELP!
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Since the equation has the x-intercept -3 and the y-intercept -5, this means the equation goes through the points (-3,0) and (0,-5)


First lets find the slope through the points (-3,0) and (0,-5)

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: is the first point (-3,0) and is the second point (0,-5))

m=%28-5-0%29%2F%280--3%29 Plug in y%5B2%5D=-5,y%5B1%5D=0,x%5B2%5D=0,x%5B1%5D=-3 (these are the coordinates of given points)

m=+-5%2F3 Subtract the terms in the numerator -5-0 to get -5. Subtract the terms in the denominator 0--3 to get 3

So the slope is
m=-5%2F3

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Now let's use the point-slope formula to find the equation of the line:



------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

y-0=%28-5%2F3%29%28x--3%29 Plug in m=-5%2F3, x%5B1%5D=-3, and y%5B1%5D=0 (these values are given)


y-0=%28-5%2F3%29%28x%2B3%29 Rewrite x--3 as x%2B3


y-0=%28-5%2F3%29x%2B%28-5%2F3%29%283%29 Distribute -5%2F3

y-0=%28-5%2F3%29x-5 Multiply -5%2F3 and 3 to get -15%2F3. Now reduce -15%2F3 to get -5

y=%28-5%2F3%29x-5%2B0 Add 0 to both sides to isolate y

y=%28-5%2F3%29x-5 Combine like terms -5 and 0 to get -5
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Answer:


So the equation of the line which goes through the points (-3,0) and (0,-5) is:y=%28-5%2F3%29x-5

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-5%2F3 and the y-intercept is b=-5

Notice if we graph the equation y=%28-5%2F3%29x-5 and plot the points (-3,0) and (0,-5), we get this: (note: if you need help with graphing, check out this solver)

drawing%28500%2C+500%2C+-10.5%2C+7.5%2C+-11.5%2C+6.5%2C%0D%0Agraph%28500%2C+500%2C+-10.5%2C+7.5%2C+-11.5%2C+6.5%2C%28-5%2F3%29x%2B-5%29%2C%0D%0Acircle%28-3%2C0%2C0.12%29%2C%0D%0Acircle%28-3%2C0%2C0.12%2B0.03%29%2C%0D%0Acircle%280%2C-5%2C0.12%29%2C%0D%0Acircle%280%2C-5%2C0.12%2B0.03%29%0D%0A%29+ Graph of y=%28-5%2F3%29x-5 through the points (-3,0) and (0,-5)

Notice how the two points lie on the line. This graphically verifies our answer.


Now let's convert the equation into standard form


Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)


y=%28-5%2F3%29%2Ax-5Start with the given equation



y%2B%285%2F3%29%2Ax=-5Add %285%2F3%29%2Ax to both sides

%2B%285%2F3%29%2Ax%2By=-5 Rearrange

3%28%2B%285%2F3%29%2Ax%2By%29=3%28-5%29 Multiply both sides by 3



3%28%2B5%2F3%29x%2B3%2Ay=3%28-5%29 Distribute



%2B%2815%2F3%29%2Ax%2B3%2Ay=-15 Multiply

%2B5%2Ax%2B3%2Ay=-15 Reduce

Now the equation is in standard form Ax%2BBy=C where A=%2B5, B=3, and C=-15





So the standard equation that x-intercept -3 and the y-intercept -5 is
5x%2B3y=-15